From edbc9f3a44b7beaae93c830a73ee73d1e01fe3a2 Mon Sep 17 00:00:00 2001
From: Gene233 <chen_jj97@163.com>
Date: Fri, 29 Mar 2024 18:08:19 +1100
Subject: [PATCH] Update vignette.

---
 vignettes/smartid_Demo.Rmd | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

diff --git a/vignettes/smartid_Demo.Rmd b/vignettes/smartid_Demo.Rmd
index c499504..a3e96ca 100644
--- a/vignettes/smartid_Demo.Rmd
+++ b/vignettes/smartid_Demo.Rmd
@@ -114,20 +114,20 @@ idf_iae_methods()
 The basic version of TF, IDF and IAE can be termed as:
 
 $\mathbf{TF_{i,j}}=\frac{N_{i,j}}{\sum_j{N_{i,j}}},$
-$\mathbf{IDF_i} = log(1+\frac{n}{n_i+1}),$
-$\mathbf{IAE_i} = log(1+\frac{n}{\sum_j^n\hat N_{i,j}+1})$
+$\mathbf{IDF_i} = \log(1+\frac{n}{n_i+1}),$
+$\mathbf{IAE_i} = \log(1+\frac{n}{\sum_j^n\hat N_{i,j}+1})$
 
 Where $N_{i,j}$ is the counts of feature $i$ in cell $j$; $\hat N_{i,j}$ is $max(0,N_{i,j}-threshold)$;
 $n$ is the total number of documents(cells); $n_i$ is $\sum_{j = 1}^{n} sign(N_{i,j} > threshold)$.
 
 Here for labeled data, we can choose logTF * IDF_prob * IAE_prob for marker identification:
-$$\mathbf{score}=logTF*IDF_{prob}*IAE_{prob}$$
+$$\mathbf{score}=\log \mathbf{TF}*\mathbf{IDF}_{prob}*\mathbf{IAE}_{prob}$$
 
 The probability version of IDF can be termed as:
-$$\mathbf{IDF_{i,j}} = log(1+\frac{\frac{n_{i,j\in D}}{n_{j\in D}}}{max(\frac{n_{i,j\in \hat D}}{n_{j\in \hat D}})+ e^{-8}}\frac{n_{i,j\in D}}{n_{j\in D}})$$
+$$\mathbf{IDF_{i,j}} = \log(1+\frac{\frac{n_{i,j\in D}}{n_{j\in D}}}{max(\frac{n_{i,j\in \hat D}}{n_{j\in \hat D}})+ e^{-8}}\frac{n_{i,j\in D}}{n_{j\in D}})$$
 
 And the probability version of IAE can be termed as:
-$$\mathbf{IAE_{i,j}} = log(1+\frac{mean(\hat N_{i,j\in D})}{max(mean(\hat N_{i,j\in \hat D}))+ e^{-8}}*mean(\hat N_{i,j\in D}))$$
+$$\mathbf{IAE_{i,j}} = \log(1+\frac{mean(\hat N_{i,j\in D})}{max(mean(\hat N_{i,j\in \hat D}))+ e^{-8}}*mean(\hat N_{i,j\in D}))$$
 
 Where $D$ is the category of cell $j$; $\hat D$ is the category other than $D$.
 
@@ -260,11 +260,11 @@ upset(fromList(c(marker_ls, marker_ls_new)), nsets = 6)
 While for the unlabeled data, `smartid` also provides the score methods with no need for label information.
 
 Here we choose logTF * IDF_sd * IAE_sd for for gene-set scoring as a use case:
-$$\mathbf{score}=logTF*IDF_{sd}*IAE_{sd}$$
+$$\mathbf{score}=\log \mathbf{TF}*\mathbf{IDF}_{sd}*\mathbf{IAE}_{sd}$$
 
 Where IDF and IAE can be termed as:
-$$\mathbf{IDF_i} = log(1+SD(TF_{i})*\frac{n}{n_i+1})$$
-$$\mathbf{IAE_i} = log(1+SD(TF_{i})*\frac{n}{\sum_{j=1}^{n}\hat N_{i,j}+1})$$
+$$\mathbf{IDF_i} = \log(1+SD(\mathbf{TF}_{i})*\frac{n}{n_i+1})$$
+$$\mathbf{IAE_i} = \log(1+SD(\mathbf{TF}_{i})*\frac{n}{\sum_{j=1}^{n}\hat N_{i,j}+1})$$
 
 ## Score Samples